In the test series, the gear oils PAO/HC/SN and PAG2 already examined with the MTM in Sect. 5 are analyzed. The coefficients of friction of these two gear oils differ very clearly in the speed range of 100–2500 mm/s by ∆μ = 0.035–0.02. The dynamic viscosity at 80 °C of PAO/HC/SN (9.03 mPas) and PAG2 (10.44 mPas) hardly differs.
A basic speed of 900 rpm was set on the drive motor, which drives the pinion gear with a rolling velocity of approximately 5800 mm/s. A sinusoidal speed fluctuation with an excitation frequency of 30 Hz was superimposed to the basic speed. This corresponds to an excitation with the 2nd engine order of a four-cylinder engine. With different angular acceleration amplitudes of the transmission input shaft, the relative angle of the meshing gear pair was recorded with the incremental encoders and plotted against time.
Fig. 6 shows the relative angle (red line) when using helical gears without torsional vibration excitation and with 1500 rad/s2 modulation on the transmission input shaft. A measured backlash jt = 0.198 mm for helical gearing is considered. Positive values of the relative angle correspond to a contact between the driven gear and the working face flanks of the driving gear. In contrast, negative values of the relative angle correspond to a contact of the driven gear on the reverse flanks during tooth meshing. A drag torque of 0.5 Nm is effective and no tension torque was applied to the brake motor. In Fig. 6a, deviations in rotation during the meshing process of the tooth pairs can be measured in the relative angle, which are caused by geometric errors, such as inaccuracies during production and assembly. Fig. 6b shows the relative angle at an angular acceleration amplitude of 1500 rad/s2 (blue line). If the angular acceleration is in the positive value range, the working face flanks of the driven gear lift off from those of the drive gear and are accelerated in the direction of the reverse flanks.
If the angular acceleration is sufficiently high, the mutual reverse flanks impact. As soon as a negative angular acceleration of the driving gear occurs, the driven gear follows this movement with a delay due to its inertia and moves back in the direction of the face flanks of the meshing teeth. In the measured circumferential backlash jt = 0.198 mm = 0.005 rad, neither the working face nor the reverse flanks are in contact with one another.
Fig. 7 shows the relative angle at an angular acceleration amplitude of 500 rad/s2 with the two different gear oils. The measured circumferential backlash is identical at jt = 0.198 mm. With 500 rad/s2 modulation, a periodic oscillation of the driven gear between the engaging reverse and working face flanks occurs. In Fig. 7a, superimposed, higher-frequency vibrations are also visible in the relative angle when using PAO/HC/SN, especially in the impacts on the working face flanks. As a result, longer, higher acceleration values occur after an impact in the course of the housing acceleration, see Fig. 7c.
This can only be explained by additional impacts of the subsequent meshing tooth pairs on the working face flanks, since the tooth meshing frequency 15of the pinion 23 Hz of the gear is lower than the excitation frequency of the torsional vibration with 30 Hz. Several successive entry impacts briefly generate high forces on the meshing tooth pairs, which lead to these high housing acceleration values. Entry impacts arise as a result of deviations from the ideal tooth flank geometry and thus from the law of gearing .
If one analyzes the maximum amplitudes of the relative angle with the measured angle of rotation of the driven gear in relation to the driving gear, it can be determined that the driven gear moves well beyond the measured circumferential backlash of jt = 0.005 rad in Fig. 7a and b. There is consequently a lengthening of the line of action, which occurs due to elastic deformation of the teeth due to the high tooth forces occurring during the impact processes. The line of action is curved in this case at the first point of contact (point (A) in Fig. 1) along the tip radius of the meshing gear. At the same time, the coefficient of friction increases at the entry impact, as the tooth tip of the wheel hits the tooth root of the pinion with a large pressure angle. The oil film is scraped away from the tooth tip and the lubrication conditions are shifted more towards boundary/mixed friction.
If one compares the behavior of the relative angle of PAO/HC/SN Fig. 7a) with the oil type PAG2 in Fig. 7b) one finds in particular the absence of the entry impacts on both the working face and reverse flanks in the relative angle. Likewise, the use of the PAG2 oil type results in a slightly higher maximum relative angular amplitude, i.e. the elastic deformation of the tooth pairs has increased with PAG2. The non-existent entry impacts lead to a lower housing acceleration with PAG2, see Fig. 7d. This behavior can be explained by the lower coefficient of friction of PAG2, which is clearly below the coefficient of friction of PAO/HC/SN in the area of boundary and mixed friction, see Fig. 4.
Fig. 8 shows the relative angle with an increase in the angular acceleration amplitude to 1500 rad/s2 with the two different gear oils. Due to the higher angular acceleration amplitude, the periodic vibration behavior between the reverse and working face flanks has remained the same for both types of gear oil, whereby the amplitude of the relative angle has increased, i.e. the tooth forces and thus the elastic deformation have become larger due to the higher angular acceleration amplitude.
With the PAO/HC/SN oil type, the occurrence of entry impacts is reduced compared to 500 rad/s2 in Fig. 7c. On the other hand, the presence of entry impacts on both the reverse flanks and on the working face flanks is greatly increased with the oil type PAG2 compared to 500 rad/s2. This leads to higher housing accelerations in comparison with the oil type PAO/HC/SN at this angular acceleration amplitude. This behavior of PAG2 cannot be explained with the friction coefficient measurements of the MTM. The contact stresses at this angular acceleration amplitude are approximately 2000 N/mm2 and above, so that they cannot be compared with the measurement conditions in Sect. 5. It can be deduced that the coefficient of friction of the tribological system also depends on the load in contact . The behavior is non-linear and can also be reversed, so that the coefficient of friction could increase again. Further investigations need to clarify this phenomenon above 1000 rad/s2.